let V be RealLinearSpace; :: thesis: for u, v, u1, v1, w, y being VECTOR of holds
( [[u,v],[u1,v1]] in DTrapezium V,w,y iff u,v,u1,v1 are_DTr_wrt w,y )
let u, v, u1, v1, w, y be VECTOR of ; :: thesis: ( [[u,v],[u1,v1]] in DTrapezium V,w,y iff u,v,u1,v1 are_DTr_wrt w,y )

now

assume [[u,v],[u1,v1]] in DTrapezium V,w,y ; :: thesis: u,v,u1,v1 are_DTr_wrt w,y
then consider u', v', u1', v1' being VECTOR of such that
A1: [u,v] = [u',v'] and
A2: [u1,v1] = [u1',v1'] and
A3: u',v',u1',v1' are_DTr_wrt w,y by Def7;
A4: u1 = u1' by A2, ZFMISC_1:33;
( u = u' & v = v' ) by A1, ZFMISC_1:33;
hence u,v,u1,v1 are_DTr_wrt w,y by A2, A3, A4, ZFMISC_1:33; :: thesis: verum

end;

hence ( [[u,v],[u1,v1]] in DTrapezium V,w,y iff u,v,u1,v1 are_DTr_wrt w,y ) by Def7; :: thesis: verum